The point-particle solution and the asymptotic flatness in 2+1 Horava gravity

Abstract

We show that the solution corresponding to the gravitational field of a point particle at rest in 2+1 nonprojectable Horava is exactly the same as its analogous in 2+1 General Relativity. This solution is well known, it is a flat cone whose deficit angle is proportional to the mass of the particle. To establish the system we couple the Horava theory to a point particle with relativistic action. As a consequence of this result, we define the condition of asymptotic flatness exactly in the same way of 2+1 General Relativity. A remarkable feature of this condition is that the dominant mode is not fixed, but affected by the mass of the configuration. Anoter important coincidence with 2+1 General Relativity under asymptotic flatness is that the energy is the same (except for some coupling constants involved), the z = 1 term with the derivative of the lapse function does not contribute.

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Cited by in corpus (8)

• Quantization of the nonprojectable 2+1D Horava theory: The second-class constraints
• BRST symmetry and unitarity of the Horava theory
• Casimir effect of a rough membrane in 2+1 Horava-Lifshitz theory
• Casimir effect in 2+1 Horava gravity
• Asymptotic flatness and nonflat solutions in the critical 2+1 Horava theory
• Exact analytic solutions in 2+1 Hořava gravity with cosmological constant
• Curvature vs degrees of freedom: The case of the critical 2+1 Horava theory
• Rotating Black Holes in Three-Dimensional Horava Gravity Revisited